1. ## Cardinality- Set theory

Hello,

I have been reading this book to brush up on what I have learned, but I the following is a bit confusing, please see if I got it correctly..

any set say
X = {dog, {} } |X| = 2
Y = {dog} |Y| = 2 ?

I figured since {} is a subset of any set, then it will be by default a part of all sets..

another one is
Z= {1,2,3,4,5} |Z| = 6 ... same reason as above ,,,

Thank you.

Best regards,
Amait

2. ## Re: Cardinality- Set theory

Originally Posted by Amait
X = {dog, {} } |X| = 2
Y = {dog} |Y| = 2 ?

I figured since {} is a subset of any set, then it will be by default a part of all sets..
The difference between the $\displaystyle X$ and $\displaystyle Y$ is that $\displaystyle \{\}$ is an element of the set $\displaystyle X$ vs $\displaystyle \{\}$ is a subset of the set $\displaystyle Y$. The cardinality of $\displaystyle X$ and $\displaystyle Y$ only counts the number of elements, NOT the number of subsets. So $\displaystyle |X|=2,|Y|=1.$ Similarly, $\displaystyle |Z|=5$

3. ## Re: Cardinality- Set theory

Thanks that is very much clear !